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Math Help - Partial Derivatives

  1. #1
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    Partial Derivatives

    I can't solve this for the life of me, so I'm appealing to the Math Help Forum! Here's the question:

    Let f(x) and g(y) be two differentiable functions and h(x,y)=f(x)+g(y) be with hx=sin(x) and hy=cos(x), and h(π/2,π/2)=5. Find h(x,y).

    I have tried and tried, but I can't seem to solve it. I know that the partial w.r.t. y of y*cos(x) will give cos(x), but what do you add to get the partial w.r.t. x to get sin(x) as well? And what about that
    h(π/2,π/2)=5 part? HELP!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    No such function exists since h = f(x) + g(y)

    hy = g ' (y) = cos(x) is a contradiction

    since g depends only on y.
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  3. #3
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    I know... I thought I was missing something, but I'm convinced now that it must be a typo on my homework... it has to be cos(y), NOT cos(x)...
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  4. #4
    MHF Contributor Calculus26's Avatar
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    I assume you'll have no pblm now but just in case:

    h(x,y) = -cos(x) + sin(y) + C

    h(pi/2,pi/2) = 1+ C = 5

    C = 4

    h(x,y) = -cos(x) + sin(y) + 4
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  5. #5
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    Hadn't got that far yet, but thanks!
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